I have two questions I'm going to be fighting the Elite 4 soon with..

Use a ThunderStone to your eevee so it can Evolve into Jolteon, In this game Jolteon is the best of the three evolution's...not including the other two. Yes it will only if you have the National Pokedex.

Eevee doesn't automatically Evolve at a certain level, unfortunantely. You need stones to evolve them into the -eon type.

Thunderstone = Jolteon
Fire Stone = Flareon
Water Stone = Vaporeon

The evolution process that would be effective would depend on who your Rival's Starter is, if you want to make something super effective agianst mainly the rival. Or if you have a Pokemon of that type (either water, fire, or thunder), then make one based on what your need is.

Blaziken is part of the National Pokedex in Fire Red. If you Trade it to a Fire Red from a Ruby (after you have obtained the Ruby and Sapphire in the Sevii Islands, of course), then Blaziken should appear in the Fire Red Pokedex. Matter of fact, Blaziken is Pokemon no. 257.

And yes, Charizard should appear in the Ruby Pokedex as well.

1) Eevee never evolves at a specific level. It will only Evolve by stones and taming (Espeon and Umbreon, only after you get the National Dex). You'll need to use the Thunderstone on Eevee to evolve it into Jolteon.

2) Yes, the Pok�mon will appear in each other's Pok�dexes, as well as Pok�mon Ruby getting the National Dex.

The only way eevee will Evolve before you beat the Elite Four is by using 1 of the three stones, after beating the elite four and after you have gotten the national dex off prof oak eevee can evolve into either umbreon or espeon by making it happy. But if you really want it to evolve into one of the three you have mentioned then a stone is the only way you can do it.

Yes it will be added to the Pokedex on fire red

Although someone mentioned Umbreon and Espeon being able to be obtained after you get the National Dex, it's just not true! They are both Friendship Evolutions, one during the day, one at night, which is why you cannot actually Evolve Eevee into either of them in FR-National Pokedex or not! You'd need to Trade Eevee over to any of R/S/E which all have time and then evolve it there. Plus, you can't trade into Ruby for a while yet, you need to beat the E4, then fix the machine for Celio on One Island with the Ruby & Sapphire stones you'll need to locate for him, and there's a few tasks along the way, too.
Why don't you like using Stones on your Pokemon? If that's the only way they Evolve, then what's the problem?? That is their only purpose, you know! And that's exactly what makes Eevee so special-you can use one of three stones to get exactly the type you want or need, or try for one of two friendship evolutions, too, in a game with a clock! If you're worried about missing moves, then just go check out a Pokedex to make sure you got all you wanted from Eevee, and then you can evolve it into whatever looks best to you at that point?